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Optical Imaging
Part 1: Telescope Optics
Part 2: Astronomical Digital Images
http://www.stecf.org/~rhook/NEON
Richard Hook
ST-ECF/ESO
24th July 2006
NEON Observing School, OHP
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Some Caveats & Warnings!
• I have selected a few topics, many things are
omitted (eg, adaptive optics)!
• I have tried to not mention material covered in
other talks (detectors, photometry,
spectroscopy…)
• I am a bit biased by my own background, mostly
Hubble imaging. I am not an optical designer.
• I have avoided getting deep into technicalities so
apologise if some material seems rather trivial.
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Part one: Telescope Optics - a very brief introduction
From the sky and through the atmosphere and telescope, but stopping just before the detector!
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Telescope designs, past, present and future
Optical characteristics
The point-spread function
The atmosphere
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The Earliest Telescopes
Galileo, ~1609
First scientific astronomical use of the telescope
Non-achromatic refractor:
>10 gain in light collecting power;
>10 gain in resolution;
compared to the human eye.
Immediately showed phases of Venus, moons of
Jupiter, stars in Milky Way, craters on the moon…
A true revolution!
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The Rise of the Reflector
Reflecting telescope invented by Newton in
late 17th century. Parabolic primary.
William Herschel, in the late 18th century
realised that aperture was the key to studying
the universe outside the solar system.
Up to late 19th century mirrors were made of
speculum metal - hard to polish and tarnished
quickly.
Use of coated glass mirrors led to further
convenience, durability and larger apertures.
Culminated in 5m Palomar telescope (1948).
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The Late-20th Century
• Telescope apertures didn’t significantly exceed 5m
between 1950 and 1990 but the transition from
photography to digital detectors led to huge improvements.
• New technology was needed for larger telescopes:
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Lighter mirrors with active control
More compact optics/tubes/domes
Altazimuth mountings
Better sites and understanding of seeing
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The Era of 8-10m (1990-2010…)
Example: ESO VLT
4 x 8.2m telescopes
Short focal ratios
Thin and actively controlled
primary
Compact alt-az mounting
Nasmyth focal stations
Compact dome (smaller than
Hale 5m dome)
Control by digital electronics
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Other technologies:
segmented mirrors (Keck),
lightweight honeycombe
(LBT), interferometry etc.
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The Evolution of Aperture
E-ELT?
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Future Telescopes I - much larger general purpose
groundbased telescope: the European ELT
Proposed three-mirror
Gregorian optical design.
D=42m, primary, aspheric f/1.
Possible mechanical structure
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Proposed five-mirror
Cassegrain optical design.
D=42m, primary aspheric f/1.
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Future telescopes II: large, widefield
groundbased survey telescopes - the LSST
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Future telescopes III: in Space: JWST
~6m effective aperture
Segmented primary mirror
Optimised for near-IR
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Passively cooled
At L2 Lagrangian point
Not serviceable
Launch in about 2013
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Basic Telescope Optical Designs
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
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Most modern
large telescopes
are variants of
the Cassegrain
design.
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Basic Properties of Telescopes Optics
Aperture = D, Focal Length=f, Focal ratio=F=f/D
For telescopes of the same design the following holds.
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Light collecting power - proportional to D2
Theoretical angular resolution - proportional to D (1.22 D)
Image scale (“/mm) - proportional to 1/f
Total flux of an object at focal plane - proportional to D2
Surface intensity of an extended source at focal plane - proportional to
1/F2
Angular Field of view - normally bigger for smaller F, wide fields need
special designs
Tube length proportional to fprimary
Dome volume (and cost?) proportional to f3primary
Cost rises as a high power (~3) of D
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Telescope Aberrations
Aberrations are deviations from a perfect optical system. They can be
due to manufacturing errors, alignment problems, or be intrinsic to the
optical design.
• There are five basic monochromatic (3rd order) aberrations:
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Spherical aberration
Astigmatism
Coma
Field curvature
Distortion
The last two only affect the position, not the quality of the image of an object.
• Systems with refractive elements also suffer from various forms of
chromatic aberration
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Optical Aberrations
Spherical
aberration
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Zernike Polynomials
Aberrations may be represented as wavefront errors
expressed as polynomial expansions in terms of angular
position (and radial distance ( on the exit pupil
he first few are:
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Why the Ritchey-Chretien?
There are many options for two-mirror telescopes:
•Classical Cassegrain - parabolic primary, hyperboloidal secondary (coma)
•Dall-Kirkham - elliptical primary, spherical secondary (easy to make, more coma)
•Ritchey-Chretien - hyperbolic primary, hyperbolic secondary (free of coma)
•All suffer from mild astigmatism and field curvature
The RC gives the best off-axis performance of a two mirror system and is used for almost all modern large telescopes:
Keck, ESO-VLT, Hubble etc.
Classical Cassegrain
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
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Ritchey-Chretien
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
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Groundbased Point-Spread Functions (PSF)
For all large groundbased telescope
imaging with long exposures the PSF is a
function of the atmosphere rather than
the telescope optics,
The image sharpness is normally given
as the “seeing”, the FWHM of the PSF in
arcsecs. 0.3” is very good, 2” is bad.
Seeing gets better at longer wavelengths.
The radial profile is well modelled by the
Moffat function:
s(r) = C / (1+r2/R2)b+ B
Where there are two free parameters
(apart from intensity, background and
position) - R, the width of the PSF and b,
the Moffat parameter. Software is
available to fit PSFs of this form.
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The radial profile of a typical
groundbased star image.
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PSFs in Space
PSFs for Hubble may be simulated using the
Tiny Tim software (included in Scisoft). It
uses a model of the telescope and Fourier
optics theory to generate high fidelity PSF
images for all of HST’s cameras. There is
also a version for Spitzer. The PSF structure
is mainly a result of diffraction and minor
optical defects. See:
www.stsci.edu/software/tinytim (V6.3)
ACS, F814W - well sampled (0.025”
pixels)
WFPC2, F300W - highly undersampled (0.1” pixels)
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Quantifying Image Quality
• FWHM of point-spread function (PSF) - measured
by simple profile fitting (eg, imexam in IRAF)
• Strehl ratio (ratio of PSF peak to theoretical
perfect value).
• Encircled energy - fraction of total flux in PSF
which falls within a given radius.
All of these need to be used with care - for example the spherically
aberrated Hubble images had excellent FWHM of the PSF core but
very low Strehl and poor encircled energy.
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Mirror coatings
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The Atmosphere - transmission
J
H
K
A
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The Atmosphere - emission
(at a good observatory sight)
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Part Two: Astronomical Digital Images
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The imaging process, with detector included
The pixel response function
Artifacts, defects and noise characteristics
Basic image reduction
Image combination, dithering and drizzling
FITS format and metadata
• Colour
• Software - the Scisoft collection
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Two Examples
A supernova at z>1 detected in
the Great Observatories Origins
Deep Survey (GOODS). z-band
imaging with Hubble ACS/WFC
at multiple epochs. Public data:
www.stsci.edu/science/udf
A small section of the Hubble Ultra Deep
Field (HUDF). The deepest optical
image of the sky ever taken (i=31). 800
orbits with HST/ACS/WFC in BViz
filters. Final scale 30mas/pix, format of
entire image 10500x10500 pixels,
FWHM of stars in combined image
80mas. Public data: www.stecf.org/UDF
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Image Formation in One Equation
I = SO P + N
Where: S is the intensity distribution on the sky
O is the optical point-spread function (PSF, including atmosphere)
P is the pixel response function (PRF) of the detector
N is noise
is the convolution operator

I is the result of sampling the continuous distribution resulting from the
convolutions at the centre of a pixel and digitising the result into DN.
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The Pixel-Response Function (P)
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The sensitivity varies across a pixel
Once produced, electrons in a CCD may
diffuse into neighbouring pixels (charge
diffusion)
The pixel cannot be regarded as a simple,
square box which fills with electrons
The example shown is for a star imaged
by HST/NICMOS as part of the Hubble
Deep Field South campaign. The centre
of the NICMOS pixels are about 20%
more sensitive than the edges
CCDs also have variations, typically
smaller than the NICMOS example
This is worse in the undersampled case
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Image Defects and Artifacts
• Cosmic-ray hits - unpredictable, numerous, bright, worse from space
• Bad pixels - predictable (but change with time), fixed to given pixels,
may be “hot”, may affect whole columns
• Saturation (digital and full-well) and resulting bleeding from bright
objects
• Ghost images - reflections from optical elements
• Cross-talk - electronic ghosts
• Charge transfer efficiency artifacts
• Glints, grot and many other nasty things
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Some real image defects (HST/WFPC2):
Bleeding
Ghost
Cosmic ray
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Charge Transfer (In)efficiency
CCDs are read out by
clocking charge along
registers. These
transfers are impeded
by radiation damage to
the chips.
This effect gets worse
with time and is worse
in space,
This image is from the
STIS CCD on Hubble.
Note the vertical tails
on stars.
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Noise
• For CCD images there are two main sources of noise:
– Poisson “shot” noise from photon statistics, applies to objects, the
sky and dark noise, increases as the square root of exposure time
– Gaussian noise from the CCD readout, independent of exposure
time
• For long exposures of faint objects through broad filters
the sky is normally the dominant noise source
• For short exposures or through narrow-band filters readout
noise can become important but is small for modern CCDs
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Geometric
Distortion
Cameras normally have
some distortion, typically a
few pixels towards the edges,
It is important to understand
and characterise it to allow it
to be removed if necessary,
particular when combining
multiple images.
Distortion may be a function
of time, filter and colour.
HST/ACS/WFC - a
severe case of distortion more than 200 pixels at
the corners. Large skew.
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Basic Frame Calibration
• Raw CCD images are normally processed by a standard pipeline to
remove the instrumental signature. The main three steps are:
– Subtraction of bias (zero-point offset)
– Subtraction of dark (proportional to exposure)
– Division by flat-field (correction for sensitivity variation)
• Once good calibration files are available basic processing can be
automated and reliable
• After this processing images are not combined and still contain cosmic
rays and other defects
• Standard archive products for some telescopes (eg, Hubble) have had
On-The-Fly Recalibration (OTFR) performed with the best reference
files
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Sampling and Frame Size
• Ideally pixels should be small enough to well sample the PSF (ie, PRF
negligible). Pixel < PSF_FWHM/2.
• But, small pixels have disadvantages:
– Smaller fields of view (detectors are finite and expensive)
– More detector noise per unit sky area (eg, PC/WF comparison)
• Instrument designers have to balance these factors and often opt for
pixel scales which undersample the PSF.
– Eg, HST/WFPC2/WF - PSF about 50mas at V, PRF 100mas.
– HST/ACS/WFC - PSF about 30mas at U, PRF 50mas.
• In the undersampled regime the PRF > PSF
• From the ground sampling depends on the seeing, instrument designers
need to anticipate the likely quality of the site.
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Image Combination
• Multiple images are normally taken of the same target:
– To avoid too many cosmic-rays
– To allow longer exposures
– To allow dithering (small shifts between exposures)
– To allow mosaicing (large shifts to cover bigger areas)
• If the multiple images are well aligned then they may be combined
easily using tools such as imcombine in IRAF which can also flag and
ignore certain image defects such as cosmic-rays
• Combining multiple dithered images, particularly if they are
undersampled is less easy…
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Undersampling and reconstruction
Truth
After pixel
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After optics
After linear reconstruction
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Dithering
• Introducing small shifts between images has several advantages:
– If sub-pixel shifts are included the sampling can be improved
– Defects can be detected and flagged
– Flat field errors may be reduced
• Most HST images are now dithered for these reasons
• How do we combine dithered, undersampled, geometrically distorted
images which have defects?
• For HST this problem arose for the Hubble Deep Field back in 1995
• It is a very general problem, affecting many observations
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Simple ways of combining dithered data
• Shift-and-add - introduces extra blurring and can’t handle
distortion, easy, fast. Useful when there are many images
and little distortion.
• Interlacing - putting input image pixel values onto a finer
output grid and using precise fractional offsets
• In all cases you need a way to measure the shifts (and
possibly rotations)
• Need something more general…
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Interlacing, nice but hard to do…
Four input images with exactly halfpixel dithers in X and Y are combined
onto an output grid with pixels half
the size by “interlacing” the input
pixels.
No noise correlation, very fast and
easy. But - doesn’t work with
geometric distortion and requires
perfect sub-pixel dithers.
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Drizzling
• A general-purpose image combination method
• Each input pixel is mapped onto the output, including geometric
distortion correction and any linear transformations
• On the output pixels are combined according to their individual
weights - for example bad pixels can have zero weight
• The “kernel” on the output can be varied from a square like the
original pixel (shift-and-add) to a point (interlacing) or, as usual,
something in between
• Preserves astrometric and photometric fidelity
• Developed for the Hubble Deep Field, used for most HST imaging
now
• Other good alternatives exist (eg, Bertin’s SWarp)
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Drizzling
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Noise in drizzled images
Drizzling, in common with other
resampling methods can introduce
correlated noise - the flux from a single
input pixel gets spread between several
output pixels according to the shape and
size of the kernel. As a result the noise in
an output pixel is no longer statistically
independent from its neighbours.
Noise correlations can vary around the
image and must be understood as they can
affect the statistical significance of
measurements (eg, photometry) of the
output.
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The Effects of Resampling Kernels
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Implemented as MultiDrizzle for HST
- www.stsci.edu/pydrizzle/multidrizzle
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FITS format and Metadata
•FITS is an almost universal data exchange format in astronomy.
•Although designed for exchange it is also used for data storage, on
disk.
•The basic FITS file has an ASCII header for metadata in the form
of keyword/value pairs followed by a binary multi-dimensional
data array.
•There are many other FITS features, for tables, extensions etc.
•For further information start at:
http://archive.stsci.edu/fits/fits_standard/
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FITS Header elements (Hubble/ACS):
SIMPLE =
T / Fits standard
BITPIX =
16 / Bits per pixel
NAXIS =
2
/ Number of axes
NAXIS1 =
4096 / Number of axes
NAXIS2 =
2048 / Number of axes
EXTEND =
T
/ File may contain extensions
ORIGIN = 'NOAO-IRAF FITS Image Kernel December 2001' / FITS file originator
IRAF-TLM= '09:10:54 (13/01/2005)'
NEXTEND =
3 / Number of standard extensions
DATE = '2005-01-13T09:10:54'
FILENAME= 'j90m04xuq_flt.fits' / name of file
FILETYPE= 'SCI
'
/ type of data found in data file
Fundamental properties:
image size, data type,
filename etc.
TELESCOP= 'HST'
/ telescope used to acquire data
INSTRUME= 'ACS '
/ identifier for instrument used to acquire data
EQUINOX =
2000.0 / equinox of celestial coord. System
……
CRPIX1 =
512.0 / x-coordinate of reference pixel
CRPIX2 =
512.0 / y-coordinate of reference pixel
CRVAL1 =
9.354166666667 / first axis value at reference pixel
CRVAL2 =
-20.895 / second axis value at reference pixel
CTYPE1 = 'RA---TAN'
/ the coordinate type for the first axis
CTYPE2 = 'DEC--TAN'
/ the coordinate type for the second axis
CD1_1 = -8.924767533197766E-07 / partial of first axis coordinate w.r.t. x
CD1_2 = 6.743481370546063E-06 / partial of first axis coordinate w.r.t. y
CD2_1 = 7.849581942774597E-06 / partial of second axis coordinate w.r.t. x
CD2_2 = 1.466547509604328E-06 / partial of second axis coordinate w.r.t. y
World Coordinate System (WCS):
linear mapping from pixel to
position on the sky.
….
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Image Quality Assessment: try this!
• Look at the metadata - WCS, exposure time etc?
• What is the scale, orientation etc?
• Look at images of point sources - how big are
they,what shape? Sampling?
• Look at the background level and shape - flat?
• Look for artifacts of all kinds - bad pixels?
Cosmic rays? Bleeding?
• Look at the noise properties, correlations?
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Colour Images
• For outreach use
• For visual scientific interpretation
The Lynx Arc
A region of intense
star formation at z>3
gravitationally lensed
and amplified by a
low-z massive cluster.
This image is an
HST/WFPC2 one
colourised with
ground-based images.
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Making Colour Images - a new
product…
Developed by Lars Christensen and collaborators:
www.spacetelescope.org/projects/fits_liberator
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Original input images
from FITS files
Colourised in
Photoshop
Final
combined
colour
version:
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Software
Scisoft is a collection of many useful
astronomical packages and tools for Linux
(Fedora Core 3) computers. A DVD is
provided in the “welcome pack”.
Most of the software mentioned in this talk
is included and “ready to run”.
Packages on the DVD include:
IRAF,STSDAS,TABLES etc
ESO-MIDAS
SExtractor/SWarp
ds9,Skycat
Tiny Tim
Python …
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That’s all - any questions?
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The Future of Space-based optical imaging?
SNAP (SuperNova
Acceleration Probe) =
JDEM (Joint Dark
Energy Mission)
Possible next widefield optical imager in
space.
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Introduction and Scope
• Optical imaging is the oldest form of astronomical data gathering, and
in some respects the simplest.
• Although astronomy has expanded into many other wavelength realms
and instrumental techniques optical imaging is still very important many of the most important recent discoveries, such as dark energy,
come from direct images in optical bands.
• This talk will introduce the subject and try to show some of the
subtleties of the imaging process and the processing of images.
• I will mostly talk about direct imaging onto array detectors, such as
CCDs and will be biased to Hubble Space Telescope and groundbased
imaging. Mostly optical, but much also applies to near IR.
• I will NOT discuss “indirect imaging”, adaptive optics imaging or the
measurement of images - photometry will be covered in detail in the
next talks.
• Finally I will introduce the Scisoft software collection.
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